Question

How do you find the product `(4x+5)(4x+5)`?

Answer 1

See a solution process below:

Explanation:

This problem can be rewritten as:

What is: `(4x + 5)^2`

This is a special form of the quadratic which can be expanded using the rule:

`(color(red)(x) + color(blue)(y))^2 = (color(red)(x) + color(blue)(y))(color(red)(x) + color(blue)(y)) = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2`

Substitute `color(red)(4x)` for `color(red)(x)` and `color(blue)(5)` for `color(blue)(y)` gives:

`(color(red)(4) + color(blue)(5))^2 = (color(red)(4) + color(blue)(5))(color(red)(4) + color(blue)(5)) = (color(red)(4x))^2 + (2 * color(red)(4x) * color(blue)(5)) + color(blue)(5)^2 = 16x^2+ 40x + 25`